Find the area of the region bounded above by y = x + 6, bounded below by y = x2, and bounded on the sides by the lines x = 0 and x = 2. Give your answer to 2 decimal places. Answer: Check

Q: Find the area of the region bounded above by y AY -x² + 8 and below by y = x². ==

A:

Q: Shade the area of the region bounded by, x² + y? p Hence, find the area of the specified region…

A: we use integration to find area between curves

Q: Find the area bounded by the lines and curves y = x? - 2 and y = 2

A: Graph:

Q: Find the area of the region bounded by 2x and the y-axis using the horizontal strip. 4 12 y² +1

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Q: What is the area of the region enclosed by the curve y=e^x and the lines x=-1 and y=3?

A:

Q: 3. Find the area of the region between y = x2 and y = 2x; approximate the area of the region using…

A: We have to solve given equations for x limits

Q: find the area of the region enclosed by the curves y=x^2-2 and y=2

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Q: Find the area of the region between y = 5x“ and y = x- + 6.

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Q: 3 a. y= 2x and y =8– 4x b. y= x°, y =8, and x= 0

A:

Q: Find the area of the region bounded by the three curves y = x², x = y³, and x + y = 2.

A: It is given that, y3=x ⇒y=x13let, y=f1(x)=x13y=x2let, y=f2(x)=x2x+y=2⇒y=2-xlet, y=f3(x)=2-x   Area…

Q: Find the area of the region bounded by x = and the y-axis using the horizontal strip. 2y²+1

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Q: Find the area of the region bounded by y = la, y = 0, x = 0, x = 2 %3D Give your answer to the…

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Q: 3) Find the area of the region enclosed by the curves: y =x, and y = 2x – x

A: For the given curves  y = x2 and y = 2x-x2  Area of the region enclosed by the above curves are…

Q: Find the area of the region bounded by y = x', x = y°, and æ + y= 2. = x²,

A: Given: y=x2 ,x=y3 and x+y=2 Graph:

Q: Find the area of the region enclosed by the curves y = |x² – 4[ and y = 4+

A: We sketch the region using a graphing calculator y=|x2-4| (green)  y=4+ x2/2 (violet)

Q: Determine the area of the region bounded by y = xvx? + 1,y = e¯i,x = -3 and the y-axis.

A:

Q: Find the area of the region between x = 2y and x = y3 — y.

A: Given x=2y and x =y3-yThe area between f(x) and g(x) are two continuous functions and  f(x)≥g(x)  on…

Q: Find the area of the region enclosed by x = y² and y = x – 2. Give your answer to 1 decimal place.

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Q: Find the area bounded by y =2x and y = 9x - x2. Sketch the region.

A:

Q: Find the area of the region between the line y = 2 - x and the x-axis, for 0 < x≤ 4.

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: Find the area of the region that is enclosed between the curves y = x² and y = x + 6.

A: The given curves are, y=x2 and y=x+6. The objective is to find the area of the region that is…

Q: Q3 Shade the area of the region bounded by, x? + y? 7 Hence, find the area of the specified region…

A: Area between curves.

Q: Find the area of the region bounded above by y = −x² + 5 and below by y = 1.

A: Given, y=-x2+5 and y=1

Q: Find the area of the region of the enclosed by the curves y = 39 – x² and y = x2 – 33.

A:

Q: Find the area of the region enclosed by the curves y = 4 24 8 16 x³ and y = 4x.

A:

Q: Find the area of the region bounded by y = 9x + 8, y = -3x + 4 and x = 14. Leave your %3D answer…

A: Area between curves

Q: Find the area of the region enclosed by the line y = 4x and the curve y = x3 + 3x?

A: Given: y=4xy=x3+3x2

Q: Find the area of the region enclosed by x=y^2 and y=x-2

A: To find the area of the region enclosed by x=y2 and y=x-2

Q: Find the area of the region bounded by x² = 1- y and y=x– 1 Hint: Use vertical strip

A:

Q: Find the area of the region in the 1s* quadrant bounded by y = x2 + 1, y = 1 – x², and x = 1. %3D

A: To find Area of the region in the 1st   quadrant bounded by y=x2+1 , y=1-x2 and x=1.

Q: Calculate the area of the region that lies under thecurve and above the  x-axis. y =2x - x2

A:

Q: Find the area of the region bounded by 2x = and the y-axis using the horizontal strip. 4 y²+1

A: We have to find the area using horizontal strip.

Q: Find the area of the region enclosed by the curves y = 7 – 2x² and y = x² + 4

A: We need to find the area of the region enclosed by the curves y=7-2x2    and    y=x2+4. Let us plot…

Q: Find the area of the region bounded by the curves 1 y = y = 4 and the x-axis using vertical strip.…

A: We have to solve given problems:

Q: Find the area of the region enclosed by the line y=4x and the curve y= x+ 3x.

A:

Q: Find the area of the region enclosed by the curves x+y=2y^2 and x+y=2

A:

Q: Calculate the area of the region that lies under thecurve and above the  x-axis. y =1- x2

A: The graphical representation of the area is,

Q: Find the area of the region bounded by x = the horizontal strip. y²+1 and the y-axis using

A: Find the area of the region bounded by x= 1/(y2+1) and the y-axis using the horizontal strip.

Q: Find the area of the region bounded by y O and Y – 8x8 + x°. -

A: First find intersection point of y=0 and y=-8x8+x9 by equating each other  ∴ -8x8+x9=0…

Q: Find the area of the region enclosed by x = y² and y = x−2.

A:

Q: Find the area of the region enclosed by the curves 4x² + y = 4 and x - y = 1.

A:

Q: 5. Find the area of the region enclosed by y = 4 – x², y = 3x and r-axis.

A:

Q: Find the area of the region inside the circle x + y = 2 and above the line y = 1. %3D

A: We have above diagram from given statement and area of yellow part , we have to find We can see…

Q: Shade the area of the region bounded by, x? + y? s p? and |x| + \y] > p Hence, find the area of the…

A: Answer

Q: Find the area of the region enclosed by the curves: y = x' – 2x², y = 2x² – 3x

A:

Q: Find the area of the region enclosed by the curves: y =x', and y= 2x-x

A: Consider the curves  y=x2y=2x−x2

Q: A. Find the area of the region between the curves y = x and y = v4 -x.

A: Area of integration problem....

Q: Find the area of the region enclosed by the two curves y = 2|x| and y = x² – 3.

A:

Q: Q1: Find the area of the region bounded by y= Vx, y v4-x and x-axis.

A:

Q: Find the area of the region bounded above by y = x + 6, bounded below by y = x², and bounded on the…

A: We need to calculate the intersection points of the given curves. So,…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.